We continue our investigation concerning the question of whether atomic bound states begin to stabilize in the ultra-intense field limit. The pulses considered are essentially arbitrary, but we distinguish between three situations. First the total classical momentum transfer is non-vanishing, second not both the total classical momentum transfer and the total classical displacement are vanishing together with the requirement that the potential has a finite number of bound states and third both the total classical momentum transfer and the total classical displacement are vanishing. For the first two cases we rigorously prove, that the ionization probability tends to one when the amplitude of the pulse tends to infinity and the pulse shape remains fixed. In the third case the limit is strictly smaller than one. This case is also related to the high frequency limit considered by Gavrila et al.
The generation of electron vortex states in ionization by intense and short laser pulses is analyzed under the scope of the lowest-order Born approximation. For near infrared laser fields and nonrelativistic intensities of the order of $10^{16}$~W/cm$^2$, we show that one has to modify the nonrelativistic treatment of ionization by accounting for recoil and mass relativistic corrections. By using the corrected quasi-relativistic theory, the requirements for the observation of electron vortex states with non-negligible probability and large topological charge are determined.
Classically allowed transport is shown to compete with quantum tunneling during the ionization of atoms by ultrashort and intense laser pulses, despite Keldysh parameters smaller than unity. This is done by comparing exact probability densities with the ones obtained from purely classical propagation using the Truncated Wigner Approximation. Not only is classical transport capable of moving trajectories away from the core, but it can also furnish ionization probabilities of the same order as the quantum ones for intensities currently employed in experiments. Our results have implications rangi…
We study theoretically the dipole radiation of a hydrogen atom driven by an intense sub-cycle pulse. The time-dependent Schrödinger equation for the system is solved by ab initio calculation to obtain the dipole response. Remarkably, a narrowband emission lasting longer than the driving pulse appears at a frequency just above the ionization threshold. An additional calculation using the strong field approximation also recovers this emission, which suggests that it corresponds to the oscillation of nearly-bound electrons that behave similarly to Rydberg electrons. The predicted phenomenon is un…
We report on tunnel ionization of Xe by 2-cycle, intense, infrared laser pulses and its dependence on carrier-envelope-phase (CEP). At low values of optical field ($E$), the ionization yield is maximum for cos-like pulses with the dependence becoming stronger for higher charge states. At higher $E$-values, the CEP dependence either washes out or flips. A simple phenomenological model is developed that predicts and confirms the observed results. CEP effects are seen to persist for 8-cycle pulses. Unexpectedly, electron rescattering plays an unimportant role in the observed CEP dependence. Our r…
Many nonlinear quantum phenomena of intense laser-atom physics can be intuitively explained with the concept of trajectory. In this paper, Bohmian mechanics (BM) is introduced to study a multiphoton process of atoms interacting with the intense laser field: above-threshold ionization (ATI). Quantum trajectory of an atomic electron in intense laser field is obtained from the Bohm-Newton equation first and then the energy of the photoelectron is gained from its trajectory. With energies of an ensemble of photoelectrons, we obtain the ATI spectrum which is consistent with the previous theoretical…
Intense-field ionization of the hydrogen molecular ion by linearly-polarized light is modelled by direct solution of the fixed-nuclei time-dependent Schrödinger equation and compared with recent experiments. Parallel transitions are calculated using algorithms which exploit massively parallel computers. We identify and calculate dynamic tunnelling ionization resonances that depend on laser wavelength and intensity, and molecular bond length. Results for $λ\sim 1064$ nm are consistent with static tunnelling ionization. At shorter wavelengths $λ\sim 790 $ nm large dynamic corrections are observe…
The alignment dependence of the ionization behavior of H$_2$ exposed to intense ultrashort laser pulses is investigated on the basis of solutions of the full time-dependent Schrödinger equation within the fixed-nuclei and dipole approximation. The total ionization yields as well as the energy-resolved electron spectra have been calculated for a parallel and a perpendicular orientation of the molecular axis with respect to the polarization axis of linear polarized laser pulses. For most, but not all considered laser peak intensities the parallel aligned molecules are easier to ionize. Furthermo…
We provide a systematic derivation of the scaling behaviour of various quantities and establish in particular the scale invariance of the ionization probability. We discuss the gauge invariance of the scaling properties and the manner in which they can be exploited as consistency check in explicit analytical expressions, in perturbation theory, in the Kramers-Henneberger and Floquet approximation, in upper and lower bound estimates and fully numerical solutions of the time dependent Schroedinger equation. The scaling invariance leads to a differential equation which has to be satisfied by the …
Visualizing intense laser field driven electron dynamics in a multielectron molecule: dynamic electron localization, bonding properties and multiple ionization bursts
In this paper we study the response in time of N$_2$, O$_2$ and F$_2$ to laser pulses having a wavelength of 390nm. We find single ionization suppression in O$_2$ and its absence in F$_2$, in accordance with experimental results at $λ= 800$nm. Within our framework of time-dependent density functional theory we are able to explain deviations from the predictions of Intense-Field Many-Body $S$-Matrix Theory (IMST). We confirm the connection of ionization suppression with destructive interference of outgoing electron waves from the ionized electron orbital. However, the prediction of ionization s…
The two- and three-body Coulomb explosion of carbonyl sulfide (OCS) by 790 nm, 50 fs laser pulses focussed to $\approx $ 10$^{16}$ Wcm$^{-2}$ has been investigated by three-dimensional covariance mapping technique. For the first time in a triatomic molecule, a single charge state, in this case the trication, has been observed to dissociate into two distinct energy channels. With the aid of a three dimensional visualization technique to reveal the ionization hierarchy, evidence is presented for the existence of two sets of ionization pathways resulting from these two initial states. While one g…
We present an analytical inversion technique which can be used to recover ionization probabilities from spatially averaged data in an N-dimensional detection scheme. The solution is given as a power series in intensity. For this reason, we call this technique a multiphoton expansion (MPE). The MPE formalism was verified with an exactly solvable inversion problem in 2D, and probabilities in the postsaturation region, where the intensity-selective scanning approach breaks down, were recovered. In 3D, ionization probabilities of Xe were successfully recovered with MPE from simulated (using the AD…
We theoretically investigate the mechanism of enhanced ionization in two-electron molecules by analyzing Bohmian trajectories for a one-dimensional H2 in an intense laser field. We identify both types of ionizing trajectories corresponding to the ejection from the up-field and down-field cores. The trajectories of the two electrons are correlated with each other in the former while correlation is negligible in the latter. The contributions from the two ionization types, though depending on laser intensity and internuclear distance, are comparable to each other.
We address the question of whether atomic bound states begin to stabilize in the short ultra-intense field limit. We provide a general theory of ionization probability and investigate its gauge invariance. For a wide range of potentials we find an upper and lower bound by non-perturbative methods, which clearly exclude the possibility that the ultra intense field might have a stabilizing effect on the atom. For short pulses we find almost complete ionization as the field strength increases.
Modern intense ultrafast pulsed lasers generate an electric field of sufficient strength to permit tunnel ionization of the valence electrons in atoms. This process is usually treated as a rapid succession of isolated events, in which the states of the remaining electrons are neglected. Such electronic interactions are predicted to be weak, the exception being recollision excitation and ionization caused by linearly-polarized radiation. In contrast, it has recently been suggested that intense field ionization may be accompanied by a two-stage `shake-up' reaction. Here we report a unique combin…
In this paper, Bohmian mechanics is introduced to the intense laser-atom physics. The motion of atomic electron in intense laser field is obtained from the Bohm-Newton equation. We find the quantum potential that dominates the quantum effect of a physical system becomes negligible as the electron is driven far away from the parent ion by the intense laser field, i.e. the behavior of the electron smoothly trends to be classical soon after the electron was ionized. Our numerical calculations present a direct positive evidence for the semiclassical trajectory methods in the intense laser-atom phy…
In the first part of this paper, the different distinguishable pathways and regions of the single and sequential double ionization are determined and discussed. It is shown that there are two distinguishable pathways for the single ionization and four distinct pathways for the sequential double ionization. It is also shown that there are two and three different regions of space which are related to the single and double ionization respectively. In the second part of the paper, the time dependent Schrödinger and Newton equations are solved simultaneously for the electrons and the nuclei of H$_2…
We present a numerical method for investigating the non-perturbative quantum mechanical interaction of light with atoms in two dimensions, without a basis expansion. This enables us to investigate intense laser-atom interactions with light of arbitrary polarization without approximation. Results are presented for the dependence of ionization and high harmonic generation on ellipticity seen in recent experiments. Strong evidence of stabilization in circular polarization is found.
The probabilities of tunnel ionization of particles confined by one-dimensional power-law and logarithmic potentials are calculated for constant and low-frequency electric fields.
The strong-field approximation can be and has been applied in both length gauge and velocity gauge with quantitatively conflicting answers. For ionization of negative ions with a ground state of odd parity, the predictions of the two gauges differ qualitatively: in the envelope of the angular-resolved energy spectrum, dips in one gauge correspond to humps in the other. We show that the length-gauge SFA matches the exact numerical solution of the time-dependent Schrödinger equation.
We investigate analytical expressions for the upper and lower bounds for the ionization probability through ultra-intense shortly pulsed laser radiation. We take several different pulse shapes into account, including in particular those with a smooth adiabatic turn-on and turn-off. For all situations for which our bounds are applicable we do not find any evidence for bound-state stabilization.
